Question

1.
p² +1
If cosec 0+ cot O=p, show that
= seco
p-1​

Answer 1

Answer:

This is the answer of the above question

Answer 2

Answer:

To prove: p^2+1/p^2-1 =sec theta

cosec theta + cot theta = p (Given)

Now, 1/sin theta + cos theta/sin theta = p

= (1 + cos theta) / sin theta = p

= (1 + cos theta) = p sin theta (Doing cross- multiplication)

= (1 + cos theta)^2 = p^2.sin^2 theta (Squaring on both sides)

= (1 + cos theta)^2 = p^2(1 - cos^2 theta) (Using formula: sin^2 theta = 1 - cos^2 theta)

= (1 + cos theta).(1 + cos theta) = p^2 . (1 + cos theta) (1 - cos theta) [Using formula: a^2 - b^2 = (a+b)(a-b)]

= (1 + cos theta) = p^2(1 - cos theta) (Cancelling 1 + cos theta on both sides)

= 1 + cos theta = p^2 - p^2 cos theta [Multiplying p^2 and (1 - cos theta)]

= cos theta + p^2cos theta = p^2 - 1

= 1/sec theta + p^2.(1/sec theta) = p^2 - 1 [Using formula: cos theta = 1/ sec theta]

= (p^2 + 1)/sec theta = p^2 - 1

= sec theta(p^2 - 1) = p^2 + 1 (Doing cross- multiplication)

= sec theta= (p^2 + 1) / (p^2 - 1)

Hence, Proved

Step-by-step explanation:

Please, give me 5 star, a thank you and mark my answer as the brainliest one.